English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $k$ be an integer with $k\geq 2$. A digraph $D$ is $k$-quasi-transitive,if for any path $x_0x_1\ldots x_k$ of length $k$, $x_0$ and $x_k$ are adjacent.Suppose that there exists a path of length at least $k+2$ in $D$. Let $P$ be ashortest path of length $k+2$ in $D$. Wang and Zhang [Hamiltonian paths in$k$-quasi-transitive digraphs, Discrete Mathematics, 339(8) (2016) 2094--2099]proved that if $k$ is even and $k\ge 4$, then $D[V(P)]$ and $D[V(D)\setminusV(P)]$ are both semicomplete digraphs. In this paper, we shall prove that if$k$ is odd and $k\ge 5$, then $D[V(P)]$ is either a semicomplete digraph or asemicomplete bipartite digraph and $D[V(D)\setminus V(P)]$ is either asemicomplete digraph, a semicomplete bipartite digraph or an empty digraph.

The structure of strong $k$-quasi-transitive digraphs with large diameters